Check if an encoding represents a unique binary string

Given an encoding of a binary string of length k, the task is to find if the given encoding uniquely identifies a binary string or not. The encoding has counts of contiguous 1s (separated by 0s).

For example, encoding of 11111 is {5}, encoding of 01101010 is {2, 1, 1} and encoding of 111011 is {3, 2}.

Examples :



Input: encoding[] = {3, 3, 3} 
       Length, k = 12 
Output: No

Explanation: There are more than one possible 
binary strings. The strings are 111011101110
and 011101110111. Hence “No” 

Input: encoding[] = {3, 3, 2} 
       Length, k = 10 
Output: Yes

Explanation: There is only one possible encoding 
that is 1110111011

A naive approach is to take an empty string and traverse through the n integers to no of 1s as given in encoding[0] and then add 1 zero to it, then encoding[1] 1s, and at the end check if the string length is equal to k then print “Yes” or print “No”

An efficient approach will be to add all the n integers to sum, and then add (n-1) to sum and check if it is equal to K, as n-1 will be the number of zeros in between every 1’s. Check if sum is equal to k, to get exactly one string or else there are more or none.

C++

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// C++ program to check if given encoding
// represents a single string.
#include <bits/stdc++.h>
using namespace std;
  
bool isUnique(int a[], int n, int k)
{
    int sum = 0;
    for (int i = 0; i < n; i++)
        sum += a[i];
      
    sum += n - 1; 
      
    // Return true if sum becomes k
    return (sum == k); 
}
  
// Driver Code
int main() 
{
  
int a[] = {3, 3, 3};
int n = sizeof(a) / sizeof(a[0]);
int k = 12;
if (isUnique(a, n, k))
    cout << "Yes";
else
    cout << "No";
return 0;
}

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Java














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// Java program to check if given encoding 


// represents a single string. 


import java.io.*; 


  


class GFG 


{ 


    static boolean isUnique(int []a, int n, int k) 


    { 


        int sum = 0; 


        for (int i = 0; i < n; i++) 


            sum += a[i]; 


          


        sum += n - 1;  


          


        // Return true if sum becomes k 


        return (sum == k);  


    } 


      


    // Driver Code 


    static public void main (String[] args) 


    { 


        int []a = {3, 3, 3}; 


        int n = a.length; 


        int k = 12; 


        if (isUnique(a, n, k)) 


            System.out.println("Yes"); 


        else


            System.out.println("No"); 


    } 


} 


  


// This code is contributed by vt_m 



















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Python3














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# Python 3 program to check if given  


# encoding represents a single string. 


  


def isUnique(a, n, k): 


    sum = 0


    for i in range(0, n, 1): 


        sum += a[i] 


      


    sum += n - 1


      


    # Return true if sum becomes k 


    return (sum == k)  


  


# Driver Code 


if __name__ == '__main__': 


    a = [3, 3, 3] 


    n = len(a) 


    k = 12


    if (isUnique(a, n, k)): 


        print("Yes") 


    else: 


        print("No") 


  


# This code is contributed by 


# Surndra_Gangwar 



















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C#














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// C# program to check if given encoding 


// represents a single string. 


using System; 


  


class GFG 


{ 


    static bool isUnique(int []a, int n, int k) 


    { 


        int sum = 0; 


        for (int i = 0; i < n; i++) 


            sum += a[i]; 


          


        sum += n - 1;  


          


        // Return true if sum becomes k 


        return (sum == k);  


    } 


      


    // Driver Code 


    static public void Main () 


    { 


        int []a = {3, 3, 3}; 


        int n = a.Length; 


        int k = 12; 


        if (isUnique(a, n, k)) 


            Console.WriteLine("Yes"); 


        else


            Console.WriteLine("No"); 


                  


    } 


} 


  


// This code is contributed by vt_m 



















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PHP














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<?php 


// PHP program to check 


// if given encoding  


// represents a single string 


  


function isUnique( $a, $n, $k) 


{ 


    $sum = 0; 


    for ($i = 0; $i < $n; $i++) 


        $sum += $a[$i]; 


      


    $sum += $n - 1;  


      


    // Return true if 


    // sum becomes k 


    return ($sum == $k);  


} 


  


// Driver Code 


$a = array(3, 3, 3); 


$n = count($a); 


$k = 12; 


if (isUnique($a, $n,$k)) 


    echo"Yes"; 


else


    echo "No"; 


      


// This code is contributed by anuj_67. 


?> 



















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Output :


No



Time complexity : O(n)

Auxiliary Space : O(1) 


This article is contributed by Striver. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.


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